UVictoria Probability and Dynamics Seminar: Eleanor Archer

A spanning tree of a finite connected graph G is a connected subgraph of G that includes every vertex and contains no cycles. In this talk we will consider uniformly drawn spanning trees of high-dimensional graphs, and explain why, under appropriate rescaling, they converge in distribution as metric-measure spaces to Aldous’ Brownian CRT. This extends an earlier result of Peres and Revelle (2004) who previously showed a form of finite-dimensional convergence. If time permits, we may also discuss scaling limits of random spanning trees with non-uniform laws. Based on joint works with Asaf Nachmias and Matan Shalev.